ON MANNHEIM PARTNER CURVES IN THREE DIMENSIONAL LIE GROUPS

Abstract

In this paper, we define Mannheim partner curves in a three dimensional Lie group G with a bi-invariant metric. The main result of the paper is given as (Theorem 4): A curve ff W I R ! G with the Frenet apparatus fT; N; B; ; g is a Mannheim partner curve if and only if 1CH 2 D 1 where , are constants and H is the harmonic curvature function of the curve ff :